Question

The points in the argand plane represented by the complex conjugates of $1+2 i, 2-3 i, 3-4 i$

• A. are collinear
• B. form an equilateral triangle
• C. form an obtuse angled triangle
• D. form an acute angled triangle

Answer 1

Answer: (C)

The complex conjugate of given points are in argand plane $A(1-2 i), B(2+3 i), C(3+4 i)$
So, $ a =B C=\sqrt{1+1}=\sqrt{2}$
$ b =C A=\sqrt{4+36}=\sqrt{40} $
$ c =A B=\sqrt{1+25}=\sqrt{26} $
$\because\, \cos B =\frac{a^{2}+c^{2}-b^{2}}{2 a c}=\frac{2+26-40}{2 \sqrt{2} \sqrt{26}} 4$
$=-\frac{12}{4 \sqrt{13}}=-\frac{3}{\sqrt{13}}<\,0 $
So, point $A, B$ and $C$ represents the vertices of an obtuse angled triangle.